According to old Trek novels, dilithium is found on Earth - but was often mislabelled as simple quartz. Many museums became rich overnight by ransacking their exhibits once dilithium's fourth-dimensional properties were discovered.

Or that dilithium, trilithium, paralithium or any of the other types of lithium crystal would be necessary ingredients for warp overall. But we know that Feds, Klingons and Romulans alike appreciate and mine the substance (even though large Romulan warships in the 24th century utilize a superior, supposedly dilithium-free power source), and that even minor cultures recognize its value, so apparently it does provide some sort of an advantage.

But it's clear there are many ways to skin this particular cat, and Cochrane might well have used one that doesn't call for any materials more exotic than the titanium for the hull.

I was always under the impression that dilithium was the most efficient fuel source for matter/anti-matter reactors. Some other type of reactor and fuel source may have been used for the Phoenix's short-range test flight.

I was always under the impression that dilithium was the most efficient fuel source for matter/anti-matter reactors. Some other type of reactor and fuel source may have been used for the Phoenix's short-range test flight.

Science isn't my strong point, but, I thought that in the fictional Trekverse, Dilithium crystals focused the matter/antimatter reaction. Duterium is the inert fuel mixed with the antimatter. I always assumed that since Cochrane's warp core is a tiny demonstrator, he must have found some other more conventional way to focus the reaction. Geordi was probably being kind by not mentioning the gross inefficiency (compared to what he's used to) of Cochrane's ship.

I just figured he somehow reconfigured the nuclear warhead to fuel the thing. Dilithium was just a power source in the 24th century. Like most cars today run on gas, but it's not the only thing in the universe that conceivably propel a car.

Why do people saw Dilithium is a fuel? All it seems to do is catalyzes the M-AM reactions.
Canonically is there any dialogue or graphic saying Dilithium or antimatter was used?

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I don't think so. The only technical bit I remember is:

LAFORGE (OC): Doctor!COCHRANE: Yeah.LAFORGE: Would you mind taking a look at this?COCHRANE: Yeah.LAFORGE: I've tried to reconstruct the intermix chamber from what I remember at school. Tell me if I got it right.COCHRANE: School? You learned about this in school?LAFORGE: Oh yeah. 'Basic Warp Design' is a required course at the Academy. The first chapter is called 'Zefram Cochrane'.COCHRANE: Well, it looks like you got it right.BARCLAY: Commander. This is what we're thinking of using to replace the damaged warp plasma conduit.
(Geordi uses his ocular implant to examine a spiral of copper tubing)LAFORGE: Yeah. Yeah, that's good, but you need to reinforce this copper tubing with a nano-polymer.

LAFORGE: The hard part's going to be calibrating the thermal curve necessary to start a controlled reaction.
RIKER: Assuming you can, can you regulate the reaction?
WESLEY: There's just enough crystal to do it. We plan to channel the reaction through the chips.
LAFORGE: Are we good?
RIKER: You're better than good. Great. Brilliant. It's going to be fun. Carry on.

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That seems to suggest that the function of the dilithium crystals is to somehow regulate the matter/antimatter reaction, rather than to provide the fuel for it.